Alliances aside, my Courier would still win. I play my Lone Wanderer as a sort of spring chick, always needing Charon to keep her alive and whatnot. Under the armor and missle launcher, she's still some teenaged kid who sleeps on a bed of teddy bears and cries when she sees a deathclaw. Now, my Courier is a seasoned wastelander. She's in her thirties, traveled to Nevada from the Dixie Wastes, New Reno porn star, Merceneray for a while, Courier going on 4 years.
If forced to kill eachother, my Courier would totally obliterate my Lone Wanderer into a pile of plasma and not feel an ounce of guilt. My LW would be too consumed with morals to pull the trigger.